Entropy-Based Solutions for Multicollinearity in Econometrics: Detection and Treatment

Entropy-Based Solutions for Multicollinearity in Econometrics: Detection and Treatment | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Entropy-Based Solutions for Multicollinearity in Econometrics: Detection and Treatment Eyas Gaffar A. Osman This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7055499/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Multicollinearity significantly compromises the reliability of econometric estimations by inflating standard errors and distorting inferential conclusions, often forcing a trade-off between model interpretability and statistical robustness. This paper introduces a novel entropy-based framework for both the detection and treatment of multicollinearity, addressing limitations of conventional methods like the Variance Inflation Factor (VIF), ridge regression, and principal component regression (PCR). We define the Entropy-Based Multicollinearity Index (EMI) as a diagnostic tool, capable of identifying both linear and non-linear dependencies by quantifying the discrepancy between aggregate marginal entropy and joint entropy. For treatment, we propose Entropy-Guided Variable Reconstruction (EGVR), a method that leverages mutual information to transform the regressor matrix, maximizing information preservation while effectively eliminating multicollinearity. Extensive Monte Carlo simulations demonstrate that EGVR consistently outperforms Ordinary Least Squares (OLS), ridge regression, and PCR in reducing Mean Squared Error (MSE) and stabilizing estimates. Furthermore, an empirical application to a real-world wage regression dataset shows EMI's superior ability to detect hidden collinearities missed by VIF, and EGVR's success in improving model fit while maintaining interpretability. This framework offers a significant advancement in econometric modeling by providing robust, interpretable solutions to the pervasive problem of multicollinearity. Keywords : multicollinearity, entropy, econometrics, regression, EMI, EGVR. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 18 Aug, 2025 Reviews received at journal 12 Aug, 2025 Reviews received at journal 06 Aug, 2025 Reviewers agreed at journal 26 Jul, 2025 Reviewers agreed at journal 26 Jul, 2025 Reviewers invited by journal 25 Jul, 2025 Editor invited by journal 24 Jul, 2025 Editor assigned by journal 10 Jul, 2025 Submission checks completed at journal 10 Jul, 2025 First submitted to journal 05 Jul, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7055499","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":491257985,"identity":"043182e1-a125-4f33-aafe-57ec16d1e217","order_by":0,"name":"Eyas Gaffar A. 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